OFFSET
0,4
COMMENTS
The Heinz numbers of these partitions are given by A371288.
EXAMPLE
The partition y = (10,5,5,5,2,2,1) has distinct parts {1,2,5,10}, which form the set of divisors of 10, so y is counted under a(30).
The a(1) = 1 through a(8) = 9 partitions:
(1) (11) (21) (31) (221) (51) (331) (71)
(111) (211) (311) (2211) (421) (3311)
(1111) (2111) (3111) (511) (4211)
(11111) (21111) (2221) (5111)
(111111) (22111) (22211)
(31111) (221111)
(211111) (311111)
(1111111) (2111111)
(11111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Union[#]==Divisors[Max[#]]&]], {n, 0, 30}]
CROSSREFS
These partitions have ranks A371288.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 22 2024
STATUS
approved